An object is placed at the centre of curvature of a concave mirror. Its image is formed at:
The centre of curvature
Understanding Image Formation by Concave Mirrors
When an object is placed in front of a concave mirror, the image formed depends on the object's position relative to the mirror's key points: the pole (P), the principal focus (F), and the centre of curvature (C).
Object Placed at the Centre of Curvature (C)
Let's analyze the scenario where an object is positioned exactly at the centre of curvature of a concave mirror. To determine the image location and characteristics, we can use ray tracing:
- Ray 1: A ray of light starting from the top of the object and traveling parallel to the principal axis strikes the mirror. After reflection, this ray passes through the principal focus (F).
- Ray 2: A ray of light starting from the top of the object and passing through the principal focus (F) strikes the mirror. After reflection, this ray becomes parallel to the principal axis.
The point where these two reflected rays intersect gives the position of the image of the top of the object. For an object placed at the centre of curvature (C), these reflected rays intersect precisely at the centre of curvature (C).
Properties of the Image Formed
When an object is placed at the centre of curvature (C) of a concave mirror, the image formed has the following characteristics:
- Position: The image is formed at the centre of curvature (C).
- Nature: The image is real (meaning it can be projected onto a screen) and inverted (upside down relative to the object).
- Size: The image is of the same size as the object.
This specific position is unique because the object and image are located at the same point, are the same size, and the image is real and inverted.
Summary of Image Location for Object at C
In summary, placing an object at the centre of curvature of a concave mirror results in the image being formed at the same location, i.e., the centre of curvature.
| Object Position | Image Position | Nature of Image | Size of Image |
|---|---|---|---|
| At C (Centre of Curvature) | At C (Centre of Curvature) | Real and Inverted | Same size as object |
Revision Table: Concave Mirror Image Formation
| Object Position | Image Position | Nature of Image | Size of Image |
|---|---|---|---|
| At Infinity | At F | Real & Inverted | Highly Diminished |
| Beyond C | Between F and C | Real & Inverted | Diminished |
| At C | At C | Real & Inverted | Same Size |
| Between C and F | Beyond C | Real & Inverted | Enlarged |
| At F | At Infinity | Real & Inverted | Highly Enlarged |
| Between F and P | Behind the Mirror | Virtual & Erect | Enlarged |
Additional Information on Concave Mirrors
A concave mirror is a converging mirror, meaning it converges rays of light that fall on it. Its inner surface is the reflecting surface. Key terms associated with a concave mirror include:
- Pole (P): The central point of the reflecting surface of the mirror.
- Principal Axis: The straight line passing through the pole and the centre of curvature.
- Principal Focus (F): A point on the principal axis where rays parallel to the principal axis converge after reflection. For a concave mirror, F is in front of the mirror.
- Centre of Curvature (C): The centre of the sphere of which the mirror is a part.
- Radius of Curvature (R): The distance between the pole and the centre of curvature ($\text{PC} = R$).
- Focal Length (f): The distance between the pole and the principal focus ($\text{PF} = f$). For a spherical mirror with a small aperture, $R = 2f$.
Concave mirrors are used in various applications, such as in headlights of cars, as shaving mirrors, and in telescopes, due to their ability to produce real, inverted, and sometimes magnified images, or to focus light.
Similar Questions
An object is placed at a distance of 20 cm from a convex lens of focal length 10 cm. The image is formed at a distance of:
When white light is dispersed by a glass prism into seven colours, out of the following colours which colour will be deviated the least?
When a ray of light travels from a denser medium to a rarer medium, it bends ________.
- If the angle of incidence formed on a concave mirror at a point is 30 ° then the angle of reflection will be:
In a concave mirror when the object is placed at infinity which of the following applies to the image?
- The line joining the centre of curvature and the pole of a given spherical mirror is called __________.
- When white light passes through a prism, different colours of light bend through different angles. Which colour bends the least and which bends the most?
- A concave mirror is used in torches and car headlights because it:
- A symmetrical biconvex lens of focal length '\(f\)' is cut into four identical pieces along and perpendicular to its principal axis The focal length of each of four pieces is
- Complete the statement with correct option.
In dispersion without deviation,_________________
Important Questions from Optics
Who was the first one to use a glass prism to obtain the spectrum of sunlight?
Twinkling of stars is due to:
In which a convex mirror is used?
A. Rear View mirrors in vehicles
B. Glass windows
C. Makeup Mirror
D. Kaleidoscope
What is the reason for formation of Mirage in desert?
An object is placed 10 cm in front of a lens. The image formed is real, inverted and of same size as the object. What is the focal length and nature of the lens?
